Bayesian Integration Using Resistivity and Lithology for Improving Estimation of Hydraulic Conductivity

Abstract The characterization of spatially heterogeneous hydraulic conductivity ( K ) is important in groundwater resources management. We propose a Bayesian statistical method that integrates multiple secondary data (continuous and category data) with primary data ( K ) to improve regional K field characterization. Considering the disparity of the data scale, spatial scarcity of primary and secondary data, and need for regional‐scale site characterization, the aquifer thickness is used as the scale for data integration. We transform the high‐resolution secondary data to the scale of K and perform linear/nonlinear regression analyses for the transformed secondary data and primary data. A Bayesian approach using Metropolis‐within‐Gibbs sampling is developed for jointly integrating the primary and transformed secondary data without a limitation on the type of data attribute and the number of data set. A synthetic example is first presented to demonstrate the capability of the proposed method. Results show that the correlation strength, not the relation type, is the primary factor for improving the estimates. The Bayesian method is applied to Choushui River alluvial fan in Taiwan. Resistivity logs and a lithological description are first upscaled and then simultaneously integrated in the K estimation. Results indicate that the improvement of the K estimate obtained using resistivity data is higher in the proximal and mid fans but lower in the distal fan compared to that obtained using lithofacies data. Jointly integrating two‐attribute data outperforms using one or no secondary data set for K estimates. The proposed Bayesian integration method is thus versatile and suitable for large‐scale aquifer characterization.